How do I get hair to follow the rig?
You need to make sure that the armature modifier is above the hair particle system in the modifier stack. If they are in the wrong order, move them up or down in the stack by clicking the arrows at the right end.


Next you need to mark Use Modifier Stack on the particle system settings. You may also need to activate Hair Dynamics, depending on exactly what you want to do. I don't use hair dynamics much, but what I can tell you about it, is that the more segments the strands have, the higher you need to set the stiffness, or the hair will fall through the emitter.
  

The movement of this sphere is controlled by a single bone, and as you can see, it follows the emitter, after setting these options. It's a bit jumpy, because I only rendered every tenth frame, and I didn't bother to make it looping endlessly, but I hope the point is clear anyway.